Stability for Take-Away Games
Palo Alto, CA 94306
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332
In this paper, we study a family of take-away games called α-TAG,
parametrized by a real number α ≥ 1.
We show that for any given α,
there is a half-open interval Iα
containing α such that the set of
losing positions for α-TAG is the same as the set of losing positions
for β-TAG if and only if β ∈ Iα.
We then end with some results and
conjectures on the nature of these intervals.
Full version: pdf,
(Concerned with sequences
Received May 8 2019; revised versions received September 25 2019; October 2 2019.
Published in Journal of Integer Sequences,
January 1 2020.
Journal of Integer Sequences home page